Tutin and Shwarts 



^■^'^[ zKd?^) ] (^«> 



At the same time, dR/dz Is required to be constant and to have the 

 value. 



. dR _ / We\ Cod) . 



^ ^ "dT - \w) 2K;(I) ^^^^ 



We leave till later a discussion of comparison with experiment, but 

 we may note now that the prediction (19) is similar to that of the 

 previous theory based on complete similarity. 



Strong Circulation (i^ » 1) . In this case the interior circu- 

 lation is very strong relative to the ideal value and the deviation from 

 the ideal vortex motion is large. The appropriate laws of motion are. 



Volume . 



^ = 4; . a'(^) {5b) 



dz 



Vorticity. 



ii^l^= - A,a'(i|j) • Wj • ij; (iOb) 



ClZ 



Momentum, 



Energy. 



(K, - Kgijj) • Wj R^ = ijj • (M^/p) (lib) 



K W-1.(W. R)^= - W.^- R • Co' (17b) 



6 dz I I '-' 



Combining (10b) and (17b) leads to the requirement that a{\\)) be 

 constant and equal to 



C 



Since similarity requires that Wg/W be constant, we may hereafter 

 take a' constant in (5b) and (iOb), Combining (5b) and (10b) leads 

 to the result 



334 



